The invention generally relates to the field of interferometry and, more particularly, to the high accuracy measurement of aspherical surfaces and wavefronts.
Aspherical surfaces have become increasingly important in modern optical systems because they offer a higher number of parameters to be optimized for enhancing the performance of a system. This can lead to systems with less surfaces, less weight, smaller dimensions and better performance, to mention only a view. Especially in fields where a high number of optical surfaces are not practical, like in astronomical telescopes or for normal incidence reflecting surfaces for the EUV wavelength of 13.6 nm used for lithography tools, it is mandatory to keep the number of surfaces as low as possible. In such cases, there is no choice but use aspherical surfaces. This is especially for the short wavelength and high quality demands placed on the performance of the complete system operating in the EUV-regime where the surface errors of the reflecting surfaces within such a system must be kept below 0.1 nm, and the measuring accuracy and precision for such errors must be even higher to be able to produce the surfaces in a deterministic manner. Also lens surfaces for lenses used in multi-element systems for lithography applications operating at wavelengths of 193 nm and 157 nm are made aspherical to lower the number of elements made of rare and expensive materials. In these cases, the departures from a best fitting sphere can be as large as 1000 xcexcm or more, and the dimensions of such lens surfaces have increased to nearly 500 mm.
The fundamental element from which optical systems are made is the single lens element. In an optical system, the function of any lens in the system is to modify the wavefront transiting this lens according to the optical design of the whole system. It is well-known that a spherical or plane wave entering such a lens emerges as an aspherical wavefront with a very high departure from the best fitting sphere, depending on the conjugates used in the particular test-configuration. So, even a single lens with either spherical or aspherical surfaces can only be tested if one is able to deal with aspherical wavefronts in a test set-up. And, it is very important to test refracting lenses in transmission because inhomogeneity of the lens material can deteriorate the wavefront even when the surfaces are free of error.
The measurement of aspherical surfaces and wavefronts increases in difficulty when the departures from the best fitting sphere become large. High precision in interferometric measurements is obtainable as the dynamic range of the measurement is made very small. To reach high precision, the wavefront of the reference wavefront, against which the aspherical wavefront is compared, has to be made aspherical as well, to ideally fit the wavefront to be measured completely. This has been done using either refractive systems, so called xe2x80x9cnull-systemsxe2x80x9d, or diffractive elements, so called xe2x80x9ccomputer generated hologramsxe2x80x9d, which alter a wave of known and measurable shape (spherical or preferably plane wave) when it transits the compensation element to fit the design aspherical surface at the location where it is designed to be placed in the test-set up.
In all these cases, the compensation element must be tested with the same rigor as the test optic to assure that the correct wavefront is delivered for comparison. This is so because the compensation element acts as a physical reference against which the final surface or part is fabricated. Therefore, unaccounted for minute flaws in the reference, while not visible in the test of the part produced with the help of that reference, in reality, will be manufactured into that part. Prominent examples exist where flaws in the reference have shown up only when the produced part failed to function properly. Consequently, It should be obvious that the same difficulties that exist in testing a test optic are also present when testing compensation elements because, again, an aspherical wavefront is produced.
Existing practices employed only indirect test methods. Refractive null-optics, which deliver the wanted wavefrontxe2x80x94or alternatively a wavefront which is close to the wanted wavefront usually deliver wavefronts that depart form their design in a well-known manner. Such null-optics are typically made solely of lenses with spherical surfaces whose radii, as well as the shape-errors, are readily measurable in a so called xe2x80x9cnull systemxe2x80x9d. Also, the refractive index of the lens material, the lens thickness and the air-spacing between the lenses may be measured carefully. The mounting of such a null-system is made with the highest precision, and it is common practice to design and fabricate them as good as possible to be thermally insensitive. However, there still remain uncertainties of the wavefront generated by the system due to temperature inhomogeneities. From actual measurements then, the theoretical wavefront which should be delivered by such a manufactured system is recalculated. When an aspherical surface is tested with the help of such a well defined null-system, the computed errors in the wavefront delivered by the system due to the errors in the individual parts of the null system are taken into account for the final result reported for the aspherical surface.
Whereas the repeatability of modern interferometric measurement methods can be made as high as fractions of a nm, the final uncertainty of the measurement performed with such a null-system is limited to about a value of tens of nm (typically 30 nm to 50 nm) because of the difficulty in knowing and controlling all influences to the level necessary for achieving fractions of nm. One can compute that, for such uncertainty, the mechanical tolerances in the mount would have to be controlled to tens of nm and that, for instance, the cleaning of the surfaces of the lenses, the index of refraction and the homogeneity of the lens material must be known better than it is possible. The homogeneity and the xe2x80x9crealxe2x80x9d refractive index of the lens material is influenced by polishing and mounting, which also introduce inner tension to the lens. Such small effects are not controllable today, and it is not possible to perform measurements of the refractive index of the final lens.
While the foregoing problems apply to indirect test methods performed with refractive null-systems, diffractive null-systems, which are called computer generated holograms, use a different fabrication technology and therefore have other problems, which will not be described here in detail. Briefly though, the uncertainty in the wavefronts generated by such diffractive null systems is of the same order of magnitude as with the refractive null systems, or even worse. In the most demanding cases, like mirrors for space telescopes or lens surfaces for lithography lens-systems, it is likely that both methods are applied and compared for their results with the refractive systems being principally used and the holograms used as a cross check. Even mechanical measurements are performed on the final produced parts as an additional cross check for the functionality of the compensation system used for interferometric tests.
Given the problems associated with the current state of the art using null compensators for interferometrically testing optics, it is a primary object of the present invention to provide a method and apparatus for high accuracy measurement of aspherical surfaces or aspherical wavefronts, either of the surface of the final optical part or the wavefront of the final optical lens element in transmission.
It is another object of the invention to lower the uncertainty of the Null-systems to an amount which is similar to the repeatability of the measurements and therefore decrease the uncertainty by a factor of roughly two orders of magnitude.
Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter when the following detailed description is read in conjunction with the drawings.
This invention relates to dispersive interferometric methods and apparatus for providing measurements of aspheric surfaces and wavefronts to enhanced accuracies.
One aspect of the invention comprises a method for measuring aspheric surfaces and wavefronts with the use of an interferometer by directing a spherical wavefront of known design at a wavelength xcex1 at a reference sphere with known measured surface properties to generate a first electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by the interferometer and directing an aspherical wavefront of known design at a wavelength xcex2 at an aspherical surface or wavefront to be tested to generate a second electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by the interferometer. The first and second electronic signals are analyzed and calculated therefrom are wavefront error maps W1=W1(xcex1) and W2=W2(xcex2), both of which contain wavelength dependent known design and measured errors and unknown errors due to the manufacture, material composition of components in the interferometer, and systematic errors. Optical path length errors caused by shape errors in the aspherical surface or wavefront are determined while accounting for substantially all error sources present in the electronic signals.
In another aspect of the invention, interferometric apparatus is provided for measuring aspheric surfaces and wavefronts and comprises an interferometer having reference and measurement legs and means positioned along said measurement leg for providing a support for alternately holding a reference sphere and an aspheric surface or means for generating an aspheric wavefront. Means for directing a spherical wavefront of known design at a wavelength xcex1 at a reference sphere with known measured surface properties are included to generate a first electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by the interferometer and for directing an aspherical wavefront of known design at a wavelength xcex2 at an aspherical surface or wavefront to be tested to generate a second electronic signal containing information about the optical path differences between the reference and measurement wavefronts generated by the interferometer. Means for analyzing the first and second electronic signals are provided and calculating therefrom wavefront error maps W1=W1(xcex1) and W2=W2(xcex2), both of which contain wavelength dependent known design and measured errors and unknown errors due to the manufacture, material composition of components in the interferometer, and systematic errors and determining the optical path error caused by shape errors in the aspherical surface or wavefront while accounting for substantially all error sources present in the electronic signals.
A single compensation lens is used in the interferometer to generate the both the spherical and aspherical wavefronts and xcex1 and xcex2, respectively. By accounting for substantially all of the sources of error, precision of a fraction of a nanometer are possible.